Thanks to recent methodological and theoretical advances, to the advent of large data sets, and to the development of ever more powerful computational schemes, Bayesian statistics have become the powerhorse of many real-world quantitative problems. The Bayesian approach is common and well accepted in areas as diverse as Genetics, Astrophysics, Linguistics, Economics, Climate sciences, etc. Bayesian methods allow for robust quantification of uncertainty of statistical inference, by computing or approximating the posterior distribution of parameters of interest in a stochastic model. They are especially attractive for complex problems where defining a prior distribution allows to add structure to parameters of large dimension, either by eliciting prior expertise on the stochastic process at hand or by using generic modelling tools such as Gaussian processes. The objective of this autumn school is to provide a comprehensive overview of Bayesian methods for complex settings: modelling techniques, computational advances, theoretical guarantees and practical implementation. A specific focus will be given on challenging applications to foster collaborations with domain experts, to identify relevant objectives and increase the impacts of all designed algorithms and presented solutions during the week.